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課程名稱 |
工程數學二
Engineering Mathematics (Ⅱ) |
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開課學期 |
105-2 |
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授課對象 |
工程科學及海洋工程學系 |
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授課教師 |
戴璽恆 |
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課號 |
ESOE2022 |
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課程識別碼 |
505 28120 |
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班次 |
02 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期一3,4(10:20~12:10)星期四7(14:20~15:10) |
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上課地點 |
工科203工科203 |
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備註 |
各組必修。
總人數上限：56人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052ESOE2022_02 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
一、課程簡介:
7. Linear Algebra: Matrices, Vectors, Determinants
Matrix multiplication, system of equations, Gauss elimination
Linear independence, rank of a matrix
Inverse of a square matrix, inverse by the adjoint matrix, Cramer's rule
8. Linear algebra: matrix eigenvalue problems
Eigenvalues, Eigenvectors
Application of Eigenvalue problems
Symmetric, skew-symmetric and orthogonal matrix
Hermitian, Skew-Hermitian, Unitary matrix
Similarity Matrices, Basis, Diagonalization
11. Fourier series, integrals and transforms
Periodic function
Fourier series
Function of any period
Half-range Expansion
Complex Fourier series
Forced oscillation
Approximation by Trigonometric polynomials
Fourier integrals
Fourier sine and cosine transforms
Fourier transforms
12. Partial differential equations
Modeling: vibrating string, wave equation
Separation of variables
D’alembert’s solution of wave equation
Heat equation: solution by Fourier series
Heat equation: solution by Fourier integral and transform
Two-dimensional wave equation
Rectangular membrane
Laplacian in Polar coordinates
Circular membrane
Laplace equation in Cylindrical and Spherical coordinates
Solutions by Laplace transform |
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課程目標 |
建立同學後續專業課程所需的數學模式建立及簡單數學模式求解的能力。 |
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課程要求 |
先修微積分 |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
Kreyszig, E."Advanced Engineering Mathematics". John Wiley & Sons,Inc. 1993. |
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參考書目 |
Kreyszig, E."Advanced Engineering Mathematics". John Wiley & Sons,Inc. 1993. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
平時成績 |
40% |
小考評量約五次 |
2. |
期中考 |
30% |
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3. |
期末考 |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/20,2/23 |
Linear Algebra, Matrices, Vectors, Determinants |
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第2週 |
2/27,3/02 |
Matrix multiplication, System of equations, Gauss elimination |
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第3週 |
3/06,3/09 |
Linear independence, Rank of a matrix |
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第4週 |
3/13,3/16 |
Linear system: general properties of solutions, inverse of a square matrix, inverse by the adjoint matrix, Cramer's rule |
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第5週 |
3/20,3/23 |
Eigenvalue problem, eigenvalues, eigenvectors |
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第6週 |
3/27,3/30 |
Symmetric, skew-symmetric and orthogonal matrix, Hermitian, Skew-Hermitian, Unitary matrix |
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第7週 |
4/03,4/06 |
Similarity matrices, basis, diagonalization |
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第8週 |
4/10,4/13 |
Fourier series, integrals and transforms |
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第9週 |
4/17,4/20 |
期中考試 |
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第10週 |
4/24,4/27 |
Half-range expansion, complex Fourier series |
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第11週 |
5/01,5/04 |
Trigonometric polynomials, Fourier sine and cosine transforms |
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第12週 |
5/08,5/11 |
Fourier transforms |
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第13週 |
5/15,5/18 |
Partial differential equations |
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第14週 |
5/22,5/25 |
Separation of variables, D'Alembert's solution |
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第15週 |
5/29,6/01 |
Heat equation: solution by Fourier series, Fourier integral and transform |
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第16週 |
6/12,6/08 |
Two-dimensional wave equation |
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第17週 |
6/12,6/15 |
Laplace equation in cylindrical and spherical coordinates |
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